The Politics of K-12 Math and Academic Rigor

The Economist:

Look around the business world and two things stand out: the modern economy places an enormous premium on brainpower; and there is not enough to go round.
But education inevitably matters most. How can India talk about its IT economy lifting the country out of poverty when 40% of its population cannot read? [MMSD’s 10th Grade Reading Data] As for the richer world, it is hard to say which throw more talent away—America’s dire public schools or Europe’s dire universities. Both suffer from too little competition and what George Bush has called “the soft bigotry of low expectations”.

Thursday’s meeting between Madison School Superintendent Art Rainwater, the MMSD’s Brian Sniff and the UW Math department included two interesting guests: UW-Madison Chancellor John Wiley [useful math links via the Chancellor’s website] and the Dean of the UW-Madison Education School. Wiley and the Ed School Dean’s attendance reflects the political nature of K-12 curriculum, particularly math. I’m glad Chancellor Wiley took time from his busy schedule to attend and look forward to his support for substantial improvements in our local math program.

Citizen agitation regarding local use of “fuzzy math” has been underway for some time. Melania Alvarez’s April, 2004 School Board campaign was based on her UW-Madison work, where she evaluated math capabilities of incoming freshman. A parent, Melania also tutored Math at Thoreau Elementary School, so she “could see both ends”. Melania discussed these campaign issues early in 2004:

  • The Madison School District’s full speed ahead implementation of Discovery Math in Elementary School, Connected Math in Middle School and Core Plus in High School despite the dismantling of these programs in Minnesota and California along with extensive local teacher and parent concerns.
  • Her discussions with MMSD Administration over their plans for these “fuzzy math” programs:

    “What happened also is I went and I talked, three years ago [2001], I went and I talked to people at the Madison Metropolitan School District and I asked them if they were trying to implement Discovery, if they were going to do, you know, Connected Math for everybody, and they told me that that was not what they were going to do. And I don’t know if that parents go . . . parents go there, they discuss, they talk with people, they will assure you you’re out there thinking that, you know, that they told you truth, and then come find later on that that’s not the case.”

    – shades Garelick’s words.

  • The role of the School Board in setting and overseeing K-12 curriculum:

    And what happens is that one of the main jobs of the School Board is to choose curriculums, set curriculums, and the implementation of those curriculums. And, unfortunately, they have not been doing that in the last year(s).

    And, of course, then the interest of the few group of educators who want to leave their mark in the world with their own system, this is the way you become famous for life. If your system, if your methodology work, then that’s it, you know, you’re remembered for generations, yeah, and so that is, so this, you know, it’s like a religion, something like that.

    And so what happens is that we have to really look at all the possibilities out there, which are being looked at. Like I said, in 19, in late ‘90s, when these curriculums were starting to be implemented, we already knew that these curriculums were controversial and they were failing. And so I am up to date to all those things.

  • Transcript | Video Interview.

I’ve heard from a number of teachers over the years who have expressed great concerns over the “downtown” math program, or “math police”.
Specifically, a group of West High’s math teachers wrote a letter to Isthmus:

At West, to address the problems of inadequate preparation, we offer an extra hour of math per day in a class called Algebra Extended. There are 11 sections of this class. This is how more kids “complete ninth grade math in the ninth grade,” not because of some touted “success” of the feeder programs in middle school.
As a matter of fact, the algebra skills and problem-solving skills of my geometry students have been generally worse every year, and my experience is echoed by many of my colleagues who teach classes beyond geometry. The kids are frustrated and angry as well, feeling, rightfully so, that it’s not their fault.

What is the Truth?

One of the challenges parents face when considering these issues is to slog through the numerous studies, rhetoric and financial interests related to curriculum. For example Mark Clayton wrote an article about the Department of Education’s math curriculum review process:

Core-Plus was one of the best of the programs reviewed, panel members say. But studies of its effectiveness were co-authored by Harold Schoen, a University of Iowa professor.
Dr. Schoen, who is listed as a co-director of the program, admits he is in line to receive royalties from the sales of Core-Plus textbooks. His studies, he says, are not motivated by the prospect of royalties, of which he has received little.
But some critics have concerns. “You simply cannot have one of your principal investigators [in a research project] also be the outside evaluator,” says R. James Milgram, a Stanford University mathematician and critic.

Click for more on the texts.

A quick look at the size of the Connected Math textbooks compared to the equivalent Singapore Math course materials illustrates the publisher and author interests in selling these large volumes irrespective of curriculum quality and rigor (not to mention the much larger potential for errors or the lost trees….).

Who is Responsible for Curriculum Decisions?

Locally, the Madison School Board, certainly the majority of the Board has generally been unwilling to wade into the curriculum oversight waters. One of the arguments put forth is that the Administration takes care of that, and they are the “experts”. Wisconsin law says otherwise; School Boards are legally responsible for curriculum:

Wisconsin Department of Public Instruction (DPI) 8.01 & Parent Barb Schrank:

Each school district board shall develop, adopt and implement a written school district curriculum plan which includes the following: a. A kindergarten through grade 12 sequential curriculum plan in each of the following subject areas: reading, language arts, mathematics, social studies, science, health, computer literacy, environmental education, physical education, art and music.

What can Parents/Citizens do?

  • Run for School Board. Three seats will be contested in April, 2007. Those positions are currently held by Johnny Winston, Jr., Shwaw Vang and Ruth Robarts (Ruth announced last spring that she would not seek re-election).
  • Send an email ( or write a letter to the Madison School Board. Mention the board’s legal curriculum responsibilities and urge them to publish a review of the current K-12 curriculum with input from Administration, Parents, Teachers and the UW Math Department. In other words, make sure that those critical of the current approach have a substantive say.
  • Ask that the District’s K-12 math curriculum materials (teacher and student) and references be published online (html format) in an easy to review manner. This information should be updated annually.
  • Advocate for school-based budgeting (a number of districts do this) and local decision making. Teachers should receive the information and tools necessary to meet the needs of all students. MMSD Teacher Barb Williams reflected on this issue in a letter to Isthmus.
  • Become active in your local PTO, or form a Math Support Group. Thoreau Elementary school has such a group for years. Math was the subject of two Thoreau PTO meetings this year. Following are my notes from the April, 2006 meeting:

    The MMSD’s Carrie Valentine gave a presentation on how the current K-5 math curriculum was developed and also displayed the new teacher guides “Learning Mathematics in the Primary Grades”. Evidently this will be distributed to principals next week.
    There were a number of useful questions, including those from a Thoreau teacher who has used Singapore Math the past few years (Barb Williams).
    The district has received a “diversity in mathematics grant”.
    The District requires (or is it the state?) that students have 1 hour of math learning per day.
    The two curriculums that they use are Growing with Math and Math Expressions.
    Barb Williams mentioned that they (her class at Thoreau) were selected to pilot Singapore math (actually a “toe dip” according to the mmsd), yet when she and her students arrived last fall (09/2005), there were no materials.
    Singapore Math evidently has been suggested as a supplement in the new teacher materials.
    One parent asked if Singapore math can be used as a core? Carrie’s response was that they did not select it because there was (has now been rectified, evidently) very little teacher training available for it. Another parent followed up and asked if the PTO could help fund teacher training in Singapore Math.
    Another parent mentioned that Singapore has differentiation materials built in, unlike everyday math which is “so shallow” that teachers end up spending lots of free time seeking and copying materials for various students.
    A parent asked if the mmsd is tracking students who have taken Singapore math as they move forward? “No.”
    A parent asked if teachers could share their method and curriculum with parents. She said it would be very helpful to know how they can help. She followed up and said the methods and curriculum change from year to year so it is hard to keep track of what’s happening.

  • Write a comment relating your K-12 math experiences on this post below.

Links & Notes:

  • The Economist – The Battle for Brainpower:

    IN A speech at Harvard University in 1943 Winston Churchill observed that “the empires of the future will be empires of the mind.” He might have added that the battles of the future will be battles for talent. To be sure, the old battles for natural resources are still with us. But they are being supplemented by new ones for talent—not just among companies (which are competing for “human resources”) but also among countries (which fret about the “balance of brains” as well as the “balance of power”)

  • Celeste Roberts on Connected Math:

    The problems with CMP go far beyond failing to reach parents. One big problem is that the edifice of mathematics is so huge. Think of how long it took mathematicians to discover all of it. When one tries to use the discovery paradigm as the sole model for math lessons, all of the time available is spent in discovery process of basic concepts. There isn’t time for more than a cursory look at any topic. There isn’t any work on hard problems related to basic concepts. There isn’t time to master computational aspects of basic concepts. Everyone learns 1/2 + 1/4, but no one learns how to find the least common denominator of 1/14 and 1/35. The people who promote a constructivist approach to math set up a false dichotomy between traditional math which teaches one to memorize formulas and tables of computations, and discovery math which teaches one to really understand how math works. I actually had a TAG resource teacher say this to me very patronizingly. “We don’t teach math anymore the way that YOU learned it. Now children really understand math when they learn it.” Excuse me, but traditional math was never like that. Tradtional math presents concepts AND teaches understanding of concepts. One learns formulas AND why they work. One also does large numbers of progressively more difficult computations to become skilled at them. The problem with traditional math is that large numbers of students don’t understand the concepts as presented and try to get by with memorizing and manipulating formulas which they don’t understand. They also don’t master the computational aspects and try to make up for this deficit by using calculators inappropriately.

  • State Educators Called Dinosaurs:

    Business and technology change rapidly. Education often changes slowly. Nearly 200 people from the southern Wisconsin business and education sectors gathered Thursday to hear an education expert talk about ways of helping education catch up.
    Willard Daggett, president and founder of the International Center for Leadership in Education in Rexford, N.Y., was the keynote presenter at a business education conference at the Comfort Inn. He introduced examples of emerging technology and noted that the job market is changing, resulting in fewer low-skill jobs and more high-technology positions.
    Daggett offered an especially critical look at education in Wisconsin. “You look more like 1970,” he said, comparing state educators to “curators preserving a museum.”

  • Promises Betrayed on the MMSD’s changing curriculum.
  • Richard Askey on MMSD 8th grade math performance.
  • Lee Sensenbrenner on Connected Math.
  • 35 Members of the UW Math Department (out of 47) wrote a letter expressing concern regarding the MMSD’s criteria for a Math Coordinator. Superintendent Art Rainwater’s reply.
  • Art Rainwater has been very active in the local Board scene (which is commendable, though I wonder if it inhibits some of the local K-12 discussion). He serves on the Board of the United Way, the Foundation for Madison Public Schools, The Minority Student Achievement Network The Collaboration Council and was formerly on SCALE’s Advisory Board (with Terry Millar, a UW professor who participated in the recent Math Forum, supporting the Districts’ program).
  • NCTM’s “Focal Points” tries to bring coherence to a national school math problem of many different State Standards. To a reasonable extent, this was influenced by successful Asian curricula, which place a greater focus on what is to be learned each year, expect students to have learned this material, and go on to other topics the next year. There is a greater emphasis on getting arithmetic solid than we have had, and this is included in “Focal Points”.
  • William Reese via Susan Troller:

    “I suspect Madison can be seen as a microcosm of what is going on throughout the rest of the country,” Reese said in a recent interview in his book-lined Bascom Hill office. “There are many extraordinarily well educated people here, and they have very high expectations of what kind of education their children are receiving.”

  • Barry Garelick:

    It was a textbook case on how to adopt substandard math textbooks. On June 15, 2005, the Washington, DC School Board voted to adopt Everyday Mathematics (EM) for elementary schools and Connected Math Program (CMP) for middle schools. The action was a photocopy of actions taken by other school boards across the country adoptions that have been occurring on a disturbingly regular basis for the past decade and a half.

    What the DCPS Board did and said on June 15 was so similar to what other school boards have done, one would think that they all operate from the same scripts:

    • A script on how to adopt math textbooks that require extensive teacher training and whose success is most likely attributable to the flurry of tutoring, enrollments in learning centers, or supplemental materials teachers must use if their students are to learn any math that will be of use.
    • A script on how to disparage testimony from mathematicians and knowledgeable parents, and give credibility only to their own witnesses.
    • A script on how to have an independent consultant summarize the results of the recommendations for textbook evaluations made by a committee hand picked by the school board.

    Like any sleight of hand, once you know the tricks, these techniques are not subtle.
    Unfortunately, many people fall prey to the illusions used to convey objectivity and professionalism in the same way Las Vegas audiences believe David Copperfield can make an automobile onstage disappear.

    Via Joanne.

Judy Newman’s recent article “Ring of Hire: Emergence of High-Tech Firms Nets Jobs – and Prestige – for Madison” notes the growth of tech employment in Dane County – echoing The Economist.

Obviously, getting math right for our future generations is critical to our social (tax base) and economic well being. An MMSD Administrator mentioned to me that they recognize the problem but believe it will take a long time to fix. It appears we have a way to go.

17 thoughts on “The Politics of K-12 Math and Academic Rigor”

  1. I finally got around the reading the NCTM Math Focal Points, published September 2006, after much fanfare regarding realignment of its ideas from “fuzzy” math to math that to most of us is more rigorous — that is, the basics.
    NCTM does acknowledge the “mile wide, inch deep” math curriculuum in the US, but in their Focal Points Question and Answers, they say:
    “Does the NCTM consider Curriculum Focal Points in any sense to be a “reversal” of its position on students learning computational skill, as has been reported in the press?
    Much of the news media got it wrong and letters have been written to newspapers. The Curriculum Focal Points are in no way a reversal of the Council’s long-standing position on teaching students to learn critical foundational topics (e.g. multiplication) with conceptual understanding, and they are in no way a retreat from Principles and Standards for School Mathematics. The Curriculum Focal Points are the next step in the implementation of the Standards. The focal points fully support the Council’s Principles and Standards for School Mathematics. In fact, the appendix in Curriculum Focal Points directly links the focal points to virtually all the expectations in Principles and Standards.”
    So much for a change in direction.
    Further, NCTM President Francis Fennell had this to say to the Wall Street Journal, criticizing WSJ interpretation of this report. Fennell writes, “Contrary to the impression left in your article, learning the basics is certainly not “new marching orders” from the NCTM, which has always considered the basic computation facts and related work with operations to be important. Nor is the new focal-points approach to curriculum development a “remarkable reversal” for NCTM. As stated in NCTM’s 1989 and 2000 standards, conceptual understanding and problem solving are absolutely fundamental to learning mathematics. The council has never promoted estimation “rather than precise answers.” Estimation is a critical component to the overall understanding and use of numbers.”
    This 50-page NCTM focal points paper is long on words, giving little rationale for these focal points — reasonable focal points, perhaps, but not justified within this document. It does not address pedagogy, it does not address or show concern as to the efficacy of the current math curriculum, and it is certainly not a change in direction. Those of us believing that a change in direction is needed will get no help from NCTM.

  2. I missed the details on “Thursday’s meeting between Madison School Superintendent Art Rainwater, the MMSD’s Brian Sniff and the UW Math department.” What was the meeting?

  3. Math Support Group:
    The Thoreau Elementary School PTO Math Support Group that was mentioned here began last school year. If you are interested in starting a discussion with other parents about math education at your school, please feel free to contact us. Bonnie Berger-Durnbaugh (email: and Rebecca Cole (email:, co-chairs of Thoreau’s Math Support Group.

  4. I attended the December 12th meeting of Madison United for Academic Excellence at which the guest speakers were Lisa Wachtel, the MMSD Director of Teaching and Learning, and the District’s new Math Coordinator.
    The most striking thing I learned at the meeting was that only 5% of the teachers teaching math in the MMSD’s 8 middle schools have secondary certification in mathematics! Even fewer of our middle school teachers are certified to teach science. In other words, almost none of our middle school teachers who are teaching our students 6th – 8th grade mathematics and science actually majored in these fields in college!
    Many of our middle school teachers are terrific teachers. However, why should we have English and social sciences majors teaching mathematics and science at the middle school level? We don’t ask them to teach Spanish, music, and PE. Providing them with a 1-week summer in-service course in the field, on occasion, doesn’t really solve the underlying problem.
    When people teach the subjects they love and studied at a high level, they can teach it with confidence and pass along to their students their love for the subject. When they get stuck teaching a subject that they, themselves, didn’t enjoy and stopped studying as soon as permitted to do so, that, too, gets transmitted to their students.
    If we truly desire to have our students prepared for algebra I when they enter 9th grade, maybe what the District really needs to do is to staff our middle school math classes with teachers certified in the field. That way, all of our middle school teachers could be teaching the subjects most dear to their hearts in which they are most knowledgeable. Everyone wins. Maybe this issue, not the specific textbooks and curricula, is the primary problem we need to fix to prepare our students to succeed in high school mathematics.

  5. FYI, The questions we submitted to Lisa and Brian (that’s Brian Sniff, MMSD K-12 Math Coordinator) will be posted soon, along with a video of their presentation.
    BTW, there are 11 middle schools in the MMSD, and those profoundly low percentages shocked even our sons! I shudder to think of the quality of pre-algebra and algebra education many of our middle school students must be getting, given that most of our middle school math teachers have only a general math background. How many students are being affected? Who knows. One of the many questions that were not answered last night was how the group of students who leave middle school having taken algebra has grown (both in size and in diversity), as a result of the end-of-fifth-grade math assessment.

  6. I share Dr. Mertz’s concern that only 5% of middle school math teachers are certified to teach math. Certification would be an important requirement.
    But, it is not clear what significance being merely certified in math truly means, or implies, regarding how well such teachers can teach math.
    Janet’s comments: “When people teach the subjects they love and studied at a high level, they can teach it with confidence and pass along to their students their love for the subject. When they get stuck teaching a subject that they, themselves, didn’t enjoy and stopped studying as soon as permitted to do so, that, too, gets transmitted to their students.”, suggests to me that teachers need more than certification, a paper that may not be worth much more than the HS diploma — yeh, you’ve passed all 12 grades.
    Teachers need to be solidly “numerate” (like “literate”).
    What I have not often seen in the Madison schools are teachers competent enough to be considered experts. (PE, music and language are obviously different).
    Whatever the teaching style, teachers need to show and model to students how to think like a mathematician, like a biologist, like a physicist, like an editor, like a historian, like a philosopher. Transmitting that level of “thinking like” knowledge (appropriate to the students’ level) takes more than mere certification.

  7. The information given was not interpreted correctly. All teachers in MMSD who teach middle school subjects are certified, only 5% are certified in secondary math, the remaining math teachers have a K-8, 1-8, 1-9 (yes, some freshman teachers may be certified to teach first grade)etc. Take a 1-8 certification, these teachers are certified to teach first grade, but also can teach ANY subject in 8th grade (they could teach art, math, phy ed etc). Because there are so many certified teachers in specific subjects (K-12 phy ed, spanish, special education) you have less teachers who are not specialized in the specials). A teacher certified in Secondary Ed English will not be teaching middle school math in the public school system, although they can in the private sector.
    Most professors at the college level have no education training, no people skills, etc. But the concern isn’t about them teaching because they have a degree in that field. They may know the subject, but stink as an educator. A principal can be originally a high school teacher, yet be the principal in the elementary level, or vice versa because they end up with a certification of K-12. A superintendent could have been a phy ed teacher, and know nothing about what it is like to teach in a core subject classroom.
    This is why often kids can not take geometry at the middle school, 8th grade teachers (who are certified elementary level through 8th grade) are certified to teach Algebra because this is a middle school and high school course, but not any higher.
    It is also not uncommon to have teachers who are say 1-8 certified and teaching at the middle school level to go back and take additional courses and even a masters in their subject, say math. The teacher is still only certified 1-8, but will have a masters or an emphasis in that subject, they just didn’t get “certified” which includes student teaching at the high school level, loose a semester of income, and probably their job placement.
    Because of the job market for teachers, I am convinced that all middle school teachers in MMSD are certified to teach the middle school subject they teach, either with an elementary certification (for all subjects) or a secondary education which does specialize in a subject. And a teacher who may have an elementary level certification, may have taken additional courses that are higher level in the subject they are teaching.
    Since about 1980, there is no longer a life time education certification, all teachers who got their certification since this time, all teachers need to take 5 credits every 6 years. This can be university credits, or credits that they can take through DPI or their school district. Teachers can choose the classes that they take, but most take classes that they think will help them in their classroom, while others will take classes to better their degree (masters in math or educational administration).

  8. Here is what I was told by a longtime District math teacher (high school):
    “Laurie – Most middle school math teachers carry a K-8 teaching license. The math requirement to get such a license is usually a general math course. The number of math certified middle school teachers in the District is about 4.”
    I replied: “Interesting. What does this mean for the teaching of algebra and geometry in our middle schools? I assume they are not covered by the general math license?”
    Answer: “It means that many of the Algebra teachers are not math certified, although the Geometry teachers (3) are. … I believe that there are 5 certified Algebra teachers [in the District].”

  9. To education4u. . . Most professors at the college have no education training or people skills, etc.??? What is your reference for that statement? I know so many teachers from kindergarden through grad school with excellent people skills and incredible knowledge of effective teaching techniques. I look forward to your reply. Marcia

  10. What I wrote was, “only 5% of the teachers teaching math in the MMSD’s 8 (stand corrected, 11) middle schools have secondary certification in mathematics!” That means many middle schools likely do not have even one teacher on staff who majored in mathematics in college. Yes, all of the District’s middle school teachers are officially certified to teach middle school, which legally enables them to teach ANY middle school subject, including math.
    Thus, it is, in theory, fine in the State of Wisconsin to have English majors who may never have even mastered algebra II teaching algebra I if they have a WI K-9 license. The question is, is this what we want for our children to provide “Success for All”? Don’t we desire to have pre-algebra and algebra I taught to our children by teachers who love mathematics and took true college-level math courses (i.e., Calculus I and above), not just K-9th math ed ones in college?
    In many other countries, math is taught to middle schoolers and, in some cases, even elementary schoolers by teachers who majored in math in college. Maybe that is part of the reason even their average students perform better than the top 10% of US students in math by 8th grade.

  11. Janet,with all due respect, teacher certification may be an issue, but I’d take a proven curriculum and an math-uncertified teacher over a math-certified teacher with a fuzzy math curriculum like Connected Math.
    If the MMSD would simply adopt a more effecitve math curriculum, say Singapore math, students would learn more.

  12. Agreed, Ed. My 4th grader brought home a “math search”, essentially a word search made up of numbers and symbols. She can read. She can do basic algebraic equations. This didn’t teach her anything, except that, in her words, “the people who created connected math are idiots, dad.” Oh well, she did learn something 😉

  13. Since licensure is a state, not district system, I would suspect that middle school teachers in other districts have the same general backgrounds (as a group)as middle school teachers in our district. I point this out only because several posts specify “Madison teachers” or “MMSD” as if our district/teachers are somehow out of the norm. The context seems important here: if Madison is unusual in its middle school staffing, than it is news to me.
    If this is going to be a point of discussion, it seems to me that it should be placed in the appropriate context–a context that is significantly broader than staffing practices of a single school district.

  14. Teacher L:
    Yes, perhaps the broader issue is why students who major in math and related subjects (engineering, for one) don’t pursue teaching as a career. The folks who put together the “New Commission on the Skills of the American Workforce” — highlighted on SIS — have some thought-provoking comments on the education workforce, and its impact on student performance.

  15. Professors are very knowledgeable about their subject, often to a fault. I hear over and over, Madison is a great grad school, but not so undergrad friendly. Many professors don’t have the people skills as I called it, to change how they explain something based on the audience. To me, being able to use vocabulary to talk to PhDs about your latest research or to a layman without talking down to either group is a people skill. I have seen math instructors with a PhDs in Math unable to teach basic algebra. The kids are more confused because the teacher can’t simplify what they are saying. In the K-12 setting it is called differentiating, and the teacher is expected to teach to the top (PhD equivalent) and bottom ends (laymen equivalent)and do it at the same time. Can you imagine having freshmen and psych grad students in the same psych class? Where would the discussions go? To me, people skills is also about being able to keep the audience attention and offering a variation of ways that information is shared for the different learning styles. I am sure most if not all of us have sat through lectures where the instructor is monotone, lectures straight from the textbook, or talks over (or below) everyone’s head. I should have been more clear.
    What I am trying to say in all this is just because someone has a higher level of education in the subject they are teaching, doesn’t make them a better teacher. I think certification is less important than the love for the subject matter and good curriculum. Certification at most if not all colleges in elementary ed, math requirements are mastery through Algebra II (Trig) in order to take the “general Math” course. I do understand that if a teacher doesn’t see the big picture, for instance feels it is okay to use calculators instead of learning their math facts, they may not realize the long term effects. I think it is less that they don’t have the knowledge, but more of a situation, if you don’t use it, you loose it. How much do any of us remember from high school or college? We remember it while it is important to us, but then we do replace the unused info with info that will meet our current interest/needs. Our society today just doesn’t look at the big pictures, we all get wrapped up in our own little worlds. And this happens everywhere including our schools, how many people do you know who are taking drugs to counteract the symptoms of other drugs…wouldn’t it have been easier to watch what they eat? Make a comment to a child that he/she will remember 20 years later? Remember something about a book we read 4-10 (or more) years ago?

  16. Interesting discussion. The worst is to have someone without math cert teaching a constructivist curriculum. Even certification is not really enough, as you need to be a master to keep the mathematical content in there, even when it is not obvious. Better not to use those curricula at all.
    At least with traditional curricula, teachers without strong math backgrounds can teach based on the models thy were taught with when they were students. Still, it would be far better if math were not taught by generalists. In high school (albeit in NYC) I do spend time unteaching mistakes that were taught in middle school.

  17. TeacherL, I agree the math certification issue is a State-wide problem, not one specific to the MMSD. Likely, it is a problem in most States in the USA. The point I was trying to make is that maybe part of the reason students in some other countries in the world are learning mathematics better than students are in the US is they learn mathematics in middle school from teachers who love the field and know it at a higher level than do most of our teachers who are teaching math in the middle schools.
    In response to Ed, I agree that the curriculum matters as well. Ideally, we should have teachers who majored in math teaching quality curricula. Our current state of non-math majors trying to teach from a “fuzzy” curriculum is the worst combination. They were neither trained themselves with this curriculum, nor are they readily able to supplement it when necessary. What happens when students in the class “discover” solutions to problems that are different from any of the answers provided in the teacher’s manual? The math major would likely be able to readily realize that the student’s alternative solution is also correct and praise the student for their novel approach. Would the English major teaching math be able to do so as well? The answer to this question is, unfortunately, frequently “no”. One consequence is lots of students who end up confused, frustrated, turned off to math, or concluding either the curriculum or their math teacher is an idiot.

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